Multivariate calibration of first-order data with the correlation constrained MCR-ALS method

• We showed that MCR answers for first-order multivariate calibrations are unique.
• Using equality/correlation constraint in MCR is necessary to obtain unique solution for multivariate calibration.
• Quantitative results obtained with MCR are as accurate as results of procedures such as PLS or PCR, etc.

In this work it is shown that soft-modeling methods can be generalized to multivariate calibration of first-order data sets.Second-order data sets are natural type of data to be analyzed with soft-modeling methods. Recently these methods, especially MCR-ALS are applied for analyzing first-order data.In first-order multivariate calibration procedures such as PLS, interferences in the unknown set are also contained in the standards used to calibrate the system.In this work the reliability of the analyte quantitations in the current multivariate calibration practices with soft-modeling method is investigated. It is shown that applying soft-modeling methods in analyzing first-order data results in unique concentration values for the analyte of interest under two main conditions: first, all the present components in the unknown set should be concluded in the calibration set. Second, the known concentration of the analyte in the calibration set should be incorporated as a constraint during the iterations.A simulated data containing three components and an experimental system with synthetic mixtures containing three artificial dyes – amaranth, tartrazine and sunset yellow – was analyzed. Grid search minimization approach was used to analyze rotational ambiguity associated to the resolution of the components present in the simulated and experimental data sets.

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